wsOFMM Diagnostics

MSE for posterior parameters: squared Euclidean distance averaged across samples

MSE of Posterior Parameter Estimates Over 20 Samples
Sampling	Model	pi (pi_posthoc)	theta	xi	Phi	K
SRS	sOFMM	0.0664	0.0627	2.4555	2.8436	0.15
SRS	wsOFMM	0.0664	0.0627	2.4555	2.8436	0.15
SRS	sOFMM Latent	0.0208 (0.0679)	0.0568	2.7338	6.7139	0.05
SRS	wsOFMM Latent	0.0208	0.0568	2.7338	6.7139	0.05
Uneq	sOFMM	0.0959	0.175	1.3909	1.4238	0.25
Uneq	wsOFMM	0.0621	0.1648	2.2284	1.94	0.25
Uneq	sOFMM Latent	0.0851 (0.1992)	0.0921	1.8757	2.2281	0.1
Uneq	wsOFMM Latent	0.0308	0.0814	1.9144	1.8859	0.1

Comparison of mean posterior estimates and variances and coverage probabilities across samples

Mean Posterior Estimates, Variance, and Coverage Over 20 Samples for Pi and Xi
Sampling	Model	Metric	pi_1	pi_2	xi_1	xi_2	xi_3	xi_4
		True	0.27425	0.72575	1.2000	-0.3300	0.0800	-0.6800
SRS	sOFMM	Mean Post Est	0.40540	0.54560	0.9246	-1.0279	0.5108	0.1346
SRS	sOFMM	Mean Post Var	0.01870	0.01970	1.4378	1.1657	1.4481	1.9010
SRS	sOFMM	Mean Coverage	1.00000	0.85000	1.0000	0.9000	0.9500	0.9000
SRS	wsOFMM	Mean Post Est	0.40540	0.54560	0.9246	-1.0279	0.5108	0.1346
SRS	wsOFMM	Mean Post Var	0.01870	0.01970	1.4378	1.1657	1.4481	1.9010
SRS	wsOFMM	Mean Coverage	1.00000	0.85000	1.0000	0.9000	0.9500	0.9000
SRS	sOFMM Latent	Mean Post Est	0.33620	0.65270	1.1013	-0.9839	0.6584	-0.0524
SRS	sOFMM Latent	Mean Post Var	0.01820	0.01850	2.2373	1.1449	2.3590	3.3044
SRS	sOFMM Latent	Mean Coverage	1.00000	0.95000	1.0000	0.9000	0.9500	1.0000
SRS	wsOFMM Latent	Mean Post Est	0.33620	0.65270	1.1013	-0.9839	0.6584	-0.0524
SRS	wsOFMM Latent	Mean Post Var	0.01820	0.01850	2.2373	1.1449	2.3590	3.3044
SRS	wsOFMM Latent	Mean Coverage	1.00000	0.95000	1.0000	0.9000	0.9500	1.0000
Uneq	sOFMM	Mean Post Est	0.43480	0.48410	1.0468	-0.7340	-0.1406	0.0074
Uneq	sOFMM	Mean Post Var	0.01510	0.01410	1.1402	0.9453	1.5140	1.1998
Uneq	sOFMM	Mean Coverage	0.60000	0.35000	1.0000	0.9500	1.0000	1.0000
Uneq	wsOFMM	Mean Post Est	0.38710	0.54910	0.8590	-0.8520	0.3815	-0.0228
Uneq	wsOFMM	Mean Post Var	0.01980	0.02010	1.0429	0.8790	1.3110	1.3963
Uneq	wsOFMM	Mean Coverage	1.00000	0.95000	1.0000	0.9000	1.0000	0.9500
Uneq	sOFMM Latent	Mean Post Est	0.45640	0.51130	1.0492	-0.8696	-0.2170	0.1574
Uneq	sOFMM Latent	Mean Post Var	0.01410	0.01340	1.3557	1.3812	2.6992	2.4441
Uneq	sOFMM Latent	Mean Coverage	0.40000	0.30000	1.0000	0.9500	0.9500	0.9000
Uneq	wsOFMM Latent	Mean Post Est	0.34640	0.62180	0.8978	-0.8494	0.4306	-0.1184
Uneq	wsOFMM Latent	Mean Post Var	0.01520	0.01570	1.4814	0.9445	1.7881	2.6873
Uneq	wsOFMM Latent	Mean Coverage	1.00000	0.90000	1.0000	0.9500	0.9500	0.9500

Mean Posterior Estimates, Variance, and Coverage Over 20 Samples for Theta (k=1)
Sampling	Model	Metric	theta1_1_1	theta1_1_2	theta2_1_1	theta2_1_2	theta3_1_1	theta3_1_2	theta4_1_1	theta4_1_2
		True	0.1000	0.9000	0.1000	0.9000	0.1000	0.9000	0.1000	0.9000
SRS	sOFMM	Mean Post Est	0.3090	0.6910	0.3403	0.6597	0.3202	0.6798	0.3481	0.6519
SRS	sOFMM	Mean Post Var	0.0423	0.0423	0.0430	0.0430	0.0403	0.0403	0.0398	0.0398
SRS	sOFMM	Mean Coverage	1.0000	1.0000	0.9500	0.9500	1.0000	1.0000	0.8500	0.8500
SRS	wsOFMM	Mean Post Est	0.3090	0.6910	0.3403	0.6597	0.3202	0.6798	0.3481	0.6519
SRS	wsOFMM	Mean Post Var	0.0423	0.0423	0.0430	0.0430	0.0403	0.0403	0.0398	0.0398
SRS	wsOFMM	Mean Coverage	1.0000	1.0000	0.9500	0.9500	1.0000	1.0000	0.8500	0.8500
SRS	sOFMM Latent	Mean Post Est	0.1913	0.8087	0.2071	0.7929	0.1927	0.8073	0.2185	0.7815
SRS	sOFMM Latent	Mean Post Var	0.0265	0.0265	0.0260	0.0260	0.0238	0.0238	0.0240	0.0240
SRS	sOFMM Latent	Mean Coverage	1.0000	1.0000	1.0000	1.0000	0.9500	0.9500	0.9000	0.9000
SRS	wsOFMM Latent	Mean Post Est	0.1913	0.8087	0.2071	0.7929	0.1927	0.8073	0.2185	0.7815
SRS	wsOFMM Latent	Mean Post Var	0.0265	0.0265	0.0260	0.0260	0.0238	0.0238	0.0240	0.0240
SRS	wsOFMM Latent	Mean Coverage	1.0000	1.0000	1.0000	1.0000	0.9500	0.9500	0.9000	0.9000
Uneq	sOFMM	Mean Post Est	0.6400	0.3600	0.6282	0.3718	0.5958	0.4042	0.6288	0.3712
Uneq	sOFMM	Mean Post Var	0.0646	0.0646	0.0650	0.0650	0.0631	0.0631	0.0687	0.0687
Uneq	sOFMM	Mean Coverage	0.6500	0.6500	0.6500	0.6500	0.6500	0.6500	0.6000	0.6000
Uneq	wsOFMM	Mean Post Est	0.4581	0.5419	0.4440	0.5560	0.3919	0.6081	0.4257	0.5743
Uneq	wsOFMM	Mean Post Var	0.0748	0.0748	0.0716	0.0716	0.0748	0.0748	0.0697	0.0697
Uneq	wsOFMM	Mean Coverage	1.0000	1.0000	0.9500	0.9500	1.0000	1.0000	0.8500	0.8500
Uneq	sOFMM Latent	Mean Post Est	0.5949	0.4051	0.6060	0.3940	0.5915	0.4085	0.6057	0.3943
Uneq	sOFMM Latent	Mean Post Var	0.0242	0.0242	0.0254	0.0254	0.0242	0.0242	0.0257	0.0257
Uneq	sOFMM Latent	Mean Coverage	0.4500	0.4500	0.4000	0.4000	0.4500	0.4500	0.4500	0.4500
Uneq	wsOFMM Latent	Mean Post Est	0.2029	0.7971	0.1921	0.8079	0.1621	0.8379	0.2000	0.8000
Uneq	wsOFMM Latent	Mean Post Var	0.0230	0.0230	0.0219	0.0219	0.0235	0.0235	0.0248	0.0248
Uneq	wsOFMM Latent	Mean Coverage	0.9500	0.9500	0.9500	0.9500	1.0000	1.0000	1.0000	1.0000

Mean Posterior Estimates, Variance, and Coverage Over 20 Samples for Theta (k=2)
Sampling	Model	Metric	theta1_2_1	theta1_2_2	theta2_2_1	theta2_2_2	theta3_2_1	theta3_2_2	theta4_2_1	theta4_2_2
		True	0.9000	0.1000	0.9000	0.1000	0.9000	0.1000	0.9000	0.1000
SRS	sOFMM	Mean Post Est	0.6471	0.3529	0.6522	0.3478	0.6431	0.3569	0.6415	0.3585
SRS	sOFMM	Mean Post Var	0.0293	0.0293	0.0280	0.0280	0.0284	0.0284	0.0276	0.0276
SRS	sOFMM	Mean Coverage	0.7500	0.7500	0.7500	0.7500	0.7500	0.7500	0.7500	0.7500
SRS	wsOFMM	Mean Post Est	0.6471	0.3529	0.6522	0.3478	0.6431	0.3569	0.6415	0.3585
SRS	wsOFMM	Mean Post Var	0.0293	0.0293	0.0280	0.0280	0.0284	0.0284	0.0276	0.0276
SRS	wsOFMM	Mean Coverage	0.7500	0.7500	0.7500	0.7500	0.7500	0.7500	0.7500	0.7500
SRS	sOFMM Latent	Mean Post Est	0.7837	0.2163	0.7836	0.2164	0.7737	0.2263	0.7820	0.2180
SRS	sOFMM Latent	Mean Post Var	0.0078	0.0078	0.0083	0.0083	0.0081	0.0081	0.0080	0.0080
SRS	sOFMM Latent	Mean Coverage	0.8500	0.8500	0.8500	0.8500	0.8500	0.8500	0.8500	0.8500
SRS	wsOFMM Latent	Mean Post Est	0.7837	0.2163	0.7836	0.2164	0.7737	0.2263	0.7820	0.2180
SRS	wsOFMM Latent	Mean Post Var	0.0078	0.0078	0.0083	0.0083	0.0081	0.0081	0.0080	0.0080
SRS	wsOFMM Latent	Mean Coverage	0.8500	0.8500	0.8500	0.8500	0.8500	0.8500	0.8500	0.8500
Uneq	sOFMM	Mean Post Est	0.4423	0.5577	0.4554	0.5446	0.4378	0.5622	0.4405	0.5595
Uneq	sOFMM	Mean Post Var	0.0148	0.0148	0.0165	0.0165	0.0157	0.0157	0.0140	0.0140
Uneq	sOFMM	Mean Coverage	0.5000	0.5000	0.5000	0.5000	0.5000	0.5000	0.5000	0.5000
Uneq	wsOFMM	Mean Post Est	0.5858	0.4142	0.5680	0.4320	0.5654	0.4346	0.5805	0.4195
Uneq	wsOFMM	Mean Post Var	0.0175	0.0175	0.0164	0.0164	0.0190	0.0190	0.0151	0.0151
Uneq	wsOFMM	Mean Coverage	0.6000	0.6000	0.6000	0.6000	0.6000	0.6000	0.6000	0.6000
Uneq	sOFMM Latent	Mean Post Est	0.4440	0.5560	0.4508	0.5492	0.4324	0.5676	0.4377	0.5623
Uneq	sOFMM Latent	Mean Post Var	0.0140	0.0140	0.0157	0.0157	0.0155	0.0155	0.0138	0.0138
Uneq	sOFMM Latent	Mean Coverage	0.5000	0.5000	0.5000	0.5000	0.5000	0.5000	0.5000	0.5000
Uneq	wsOFMM Latent	Mean Post Est	0.8258	0.1742	0.8094	0.1906	0.7956	0.2044	0.8009	0.1991
Uneq	wsOFMM Latent	Mean Post Var	0.0202	0.0202	0.0207	0.0207	0.0222	0.0222	0.0223	0.0223
Uneq	wsOFMM Latent	Mean Coverage	0.8500	0.8500	0.9000	0.9000	0.9000	0.9000	0.9000	0.9000

MCMC diagnostic plots for select samples

Population scenario 2, SRS

Population scenario 2, SRS, latent

Population scenario 2, unequal sampling

Population scenario 2, unequal sampling, latent

Diagnostics across samples

Non-latent version

wsOFMM Diagnostics

Stephanie Wu

3/26/2022

MSE for posterior parameters: squared Euclidean distance averaged across samples

Comparison of mean posterior estimates and variances and coverage probabilities across samples

MCMC diagnostic plots for select samples

Population scenario 2, SRS

Population scenario 2, SRS, latent

Population scenario 2, unequal sampling

Population scenario 2, unequal sampling, latent

Diagnostics across samples

Non-latent version